This can actually be done by manipulating the search URL. See the tutorial wiki here:https://forum.inaturalist.org/t/how-to-use-inaturalists-search-urls-wiki/63
For example, this should show all Parulids in California except Setophaga coronata:
https://www.inaturalist.org/observations/identify?taxon_id=71349&place_id=14&without_taxon_id=145245
So it’s there, just not in the user interface.